Fig. REF (a) shows the stress-strain curves for the parameter set \(s_p-s_t-s_a\) . Under stretching of GNRS system, the stress values remain low up to a strain of 0.3. This behavior is in contrast to that of pristine graphene. The given deformation stretches the bond lengths in pristine graphene and increases the stress levels. In GNRS systems, the given deformation deflects the atomic system instead of stretching the bonds, which is similar to the earlier observations for graphene kirigami [1]}. Further, the recent study on nonlinear vibrations for helical graphene nanoribbon shows a transformation of softening type to hardening type response between the amplitude to frequency variation during the increase in mechanical loading[2]}. In GNRS, the initial plateau in stress-strain curve up to a strain of \(0.3\)  corresponds to the soft nonlinearity. Because of the transformation from softening to hardening type natural vibrations, GNRS system start stretching due to the increased loading. Fig. REF (a) visualizes the initial (strain is 0) atomic configuration for \(18-3.2-5\)  GNRS. Visual molecular dynamics package [3]} has been used to generate the atomic snapshots. At a strain of 0.18, because of the deflections, a higher number of crests and troughs are observed in Fig. REF (b). Further straining to 0.30, deflects the GNRS without increasing the peaks (Fig. REF (c)). For strain less than 0.30, there is no significant increase in the stress distributions. When strain is more than 0.30, there is an increase in stress due to the bond stretching. Fig. REF (d) shows the locations of stress concentrations (near peaks) in the atomic configurations. Atomic configuration in Fig. REF (e) shows the multiple bond failures at strain 0.54. The failure process for other members in this parameter set is similar to the configuration \(18-3.2-5\)  GNRS. However, there are differences in the tensile strength (TS) and onsite of failure/rupture strain (RS) values due to the changes in the geometrical parameters. We use arc length as the variable to discuss the parametric dependence of RS and TS on \(s_p\) , \(s_t\)  and \(s_a\) . Fig. REF (d) shows that RS is nearly converged to 0.45 for arc lengths larger than 170 nm. Whereas, TS has a very large variation with arc length, from 33 to 7 GPa, which is due to the increase of parameter \(s_t\)  in GNRS design. As \(s_t\)  increases, the interaction between stress centers near crest and troughs of GNRS decreases, which decrease the total system stress. Further increase in the size parameters will converge to a constant value. Finally, for GNRS systems, the stress concentrates near the peak portions lead to global failure by breaking the bonds in carbon rings. The RS for the experimentally manufactured GNRS is about \(0.35\)  for a system with thickness 50 nm [4]}. This observation is in close agreement with the converged RS value of \(0.43\)  for spring design, which shows that our simulation predictions are accurate enough to explore the theoretical understanding for these novel design.
